Second-order variational analysis in second-order cone programming.

*(English)*Zbl 1440.90079Summary: The paper conducts a second-order variational analysis for an important class of nonpolyhedral conic programs generated by the so-called second-order/Lorentz/ice-cream cone \({\mathcal{Q}}\). From one hand, we prove that the indicator function of \({\mathcal{Q}}\) is always twice epi-differentiable and apply this result to characterizing the uniqueness of Lagrange multipliers together with an error bound estimate in the general second-order cone programming setting involving twice differentiable data. On the other hand, we precisely calculate the graphical derivative of the normal cone mapping to \({\mathcal{Q}}\) under the metric subregularity constraint qualification and then give an application of the latter result to a complete characterization of isolated calmness for perturbed variational systems associated with second-order cone programs. The obtained results seem to be the first in the literature in these directions for nonpolyhedral problems without imposing any nondegeneracy assumptions.

##### MSC:

90C31 | Sensitivity, stability, parametric optimization |

49J52 | Nonsmooth analysis |

49J53 | Set-valued and variational analysis |

##### Keywords:

second-order conic programs; nonpolyhedral systems; error bounds; second-order variational analysis; twice epi-differentiability; graphical derivative; isolated calmness
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\textit{N. T. V. Hang} et al., Math. Program. 180, No. 1--2 (A), 75--116 (2020; Zbl 1440.90079)

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